Isometric immersions of space forms in space forms

Spherical Minimal Immersions of Spherical Space Forms

Introduction. A number of authors [C], [DW1], [DW2], [L], [T] have studied minimal isometric immersions of Riemannian manifolds into round spheres, and in particular of round spheres into round spheres. As was observed by T. Takahashi [T], if Φ:M → S(r) ⊂ R is such a minimal immersion, then the components of Φ must be eigenfuctions of the Laplace operator on M for the same eigenvalue. And conve...

Umbilicity of (Space-Like) Submanifolds of Pseudo-Riemannian Space Forms

We study umbilic (space-like) submanifolds of pseudo-Riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo Euclidean space and relate this notion to umbilicity. Finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.A pseudo-Riemannian submanifold M in (a...

Isotropic Lagrangian Submanifolds in Complex Space Forms

In this paper we study isotropic Lagrangian submanifolds , in complex space forms . It is shown that they are either totally geodesic or minimal in the complex projective space , if . When , they are either totally geodesic or minimal in . We also give a classification of semi-parallel Lagrangian H-umbilical submanifolds.

Generalized Dpw Method and an Application to Isometric Immersions of Space Forms

Let G be a complex Lie group and ΛG denote the group of maps from the unit circle S into G, of a suitable class. A differentiable map F from a manifold M into ΛG, is said to be of connection order (ba) if the Fourier expansion in the loop parameter λ of the S-family of Maurer-Cartan forms for F , namely F λ dFλ, is of the form P b i=a αiλ . Most integrable systems in geometry are associated to ...

Minimal Lagrangian isotropic immersions in indefinite complex space forms